Can't go wrong with a used Civic. For $3000, you can probably get a late 90's or early 00's model, coupe or sedan. Or a Toyota Corolla.
For really old cars over 50K miles, some things to look for..
- Make sure the owner changed the timing belt. It's pretty common to get them replaced at 70K miles. If the owner hasn't done change it, then it's probably going to be $600 at the dealer for timing belt, accessory belt, and water pump. But it should run around $300 at an independent garage. The belt itself is cheap. It's just a very time consuming process and that's why it costs so much.
- Look for leaks around the top of the engine. Assuming that the previous owner hasn't steam cleaned the engine, if you see oil/gunk build-up, then the cylinder head gasket needs to be replaced.
- Look for leaks on the ground where it's parked. On old cars, there could be leaks from the radiator or oil pan gasket or oil pan spigot or CV boots or brake lines.
- Make sure the car is cold before you check this. Unscrew the radiator cap and check for weird colors. If you see red or brown, then there might be corrosion in the radiator.
- If you're looking for a manual car, ask when the clutch has been replaced. Usually clutches should be replaced after 75K of normal driving. You should be able to tell if the clutch is worn, by test driving it. If you're looking for an automatic, there's not much to check. Take it for a test drive and see if the auto transmission shifts smoothly. If it seems jerky. Or if it keeps hunting for gears, then there might be something wrong.
- Carefully inspect the outside of the car. Try to view it on a clear sunny day. If you see masking lines or uneven paint color or uneven shine, then it means it had some body work done. Could be a major collision or could be just a parking lot fender bender. Either way, ask about it.
- Be suspicious of over usage of air fresheners. It means the car stinks inside for whatever reason.. moisture leak, smoker, dead animal somewhere, old burger dropped under the seat, and so on.